The following proper inclusions are known: Every \(2k\) -planar graph
is \(k\) -gap planar, which in turn is \(2k\)\(+\) 2-quasi-planar
[1]}. Every RAC graph is fan-crossing free and
quasi-planar [2]}. Every fan-crossing graph is
quasi-planar [3]}. In addition, the following
incomparabilities are known: (i) 1-planar and RAC
[4]} (ii) 2-planar and fan-crossing (fan-planar)
[5]}, and (iii) fan-crossing and 1-gap-planar, where
the latter, stated as an open problem in [1]}, follows
from \(K_8\)  and \(K_{4, n}\)  for \(n \ge 9\)  [7]}.
